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Quantitative Research Methods Summative Assignment Overall word limit, 3,000 words maximum (excluding tables/figures) Question 1 a) A financial analyst specializes in the stocks of the NASDAQ and produces end-of-the-year evaluations of their performance. Running her evaluations at the end of December 2007, she discovers that the return of: 一42% of the stocks was higher than the return of the NASDAQ index 一22% of the stocks was lower than the return of the NASDAQ index 一36% of the stocks was about the same as the return of the NASDAQ index. 75% of the stocks that performed better than the NASDAQ were designated as "recommended buys", as were 50% of those that performed about as well as the NASDAQ and 15% of those that performed worse. What is the probability that a stock that was a "recommended buy" outperformed the NASDAQ? (5 marks) b) Suppose the probability that the NASDAQ index will rise over any given month during a year is 0.5. If we assume that the performance of the index on any month is independent from its performance on the previous month, calculate the following: i) the probability that a rise in the index will be observed in at least four out of the twelve months ii) the probability that a rise in the index will be observed in at most nine months iii) the probability that a rise in the index will be observed in at least one month iv) the probability that a rise in the index will be observed in no month (5 marks) c) The security department of Durham University wants to know whether or not the average time required by a night porter to walk his round, µ, is 45 minutes. A random sample of 50 rounds is observed, and the average time needed by the night porter to walk his round is 46.8 minutes with a sample standard deviation of 2 minutes. i) Formulate an appropriate null and alternative hypothesis ii) Construct the relevant test statistic iii) Would you reject or "accept" the null hypothesis at the 5 per cent level of significance? (5 marks) d) Suppose incomes in a population are normally distributed with mean $15,000 and standard deviation $5,000. i) Assume that a family is considered "poor" if its income falls below $8,000. What is the proportion of poor families in the population? ii) Let us define "poor" as those families that fall into the lowest 12 per cent of the income distribution. What is the level of income below which a family is considered to be poor? (5 marks) Question 2 Each of you has been allocated the monthly time series of the closing prices of the NASDAQ index as well as one of its current constituent stocks for the January 2000--December 2007 period (96 monthly observations). a) Obtain descriptive statistics on the time series of log-differenced returns for both the NASDAQ as well as the selected stock and comment on them. (5marks) b) Using the single-factor Capital Asset Pricing Model R¡,t - Rf,t = a + β( Rm,t - Rf,t ) +ε¡,t where R¡,t is the return on the selected stock, Rf,t is the 3 month treasury bill rate and Rm,t is the return on the NASDAQ: i) obtain estimates for the a andβcoefficients and critically comment on them ii) critically discuss the presence or absence in your results of the regression anomalies known as